### hu_e_wilson - Arkansas Space Grant Consortium

```Designing a High Resolution Fiber-Fed
Spectrograph for Solar Observations
Edmond Wilson
Brennan Thomason
Stephanie Inabnet
Tamara Reed
Harding University
Project Goal
Design a spreadsheet program to aid in
optimizing the light throughput of a CzernyTurner Spectrograph fed by an optical fiber
Czerny-Turner Monochromator Configuration
http://terpconnect.umd.edu/~toh/models/Monochromator.png
The model for our instrument is based on the discussion in Chapter 1 of
the book, Guide for Spectroscopy, by Jobin Yvon/SPEX, 1994. Figure 1
below was created from Figure 3 in the book, with errors in the original
figure corrected. Although the light path of a Czerny-Turner
spectrometer is usually folded, mathematically, it can be treated as if
the light path were arranged linearly without changing the results.
Equivalent Optical Path for Czerny-Turner Spectrometer
Begin with a grating….
Plane Grating Dimensions
Richardson Grating Laboratories, Grating Model Number
290-R
Enter Diffraction Order to Be Used in Calculations, k
Enter height of grating in mm, hG
Enter width of grating in mm, wG
Enter thickness of grating in mm & inches
Enter groove density of grating in grooves/mm, n
Enter Blaze wavelength in Littrow configuration in nm
Enter Nominal blaze angle in degrees
Given
1 Given
58 Given
58
6
1800
500
26.7
Given
Given
Given
Given
Given
Collimating Mirror Next
Collimating Mirror Dimensions
Enter parabolic mirror diameter in mm
64.00
Given
320.00
Given
Parabolic mirror focal length in inches
12.60
Calculated
Enter parabolic mirror edge thickness in mm
19.10
Given
5.00
Calculated
Enter parabolic mirror focal length in mm
Aperture, f/# (Calculated)
Camera
Camera Mirror Dimensions
Enter parabolic mirror diameter in mm
64.00
Given
320.00
Given
Parabolic mirror focal length in inches
12.60
Calculated
Enter parabolic mirror edge thickness in mm
19.10
Given
5.00
Calculated
Enter parabolic mirror focal length in mm
Aperture, f/# (Calculated)
Slit Parameters
Slit Dimensions
Enter Fixed Slit Height in mm, h
0.2987
Given
Enter Fixed Slit Width in µm, w =bandpass/dispersion, mm
15
Given
Spectral Bandpass desired, nm
0.5
Fiber Parameters
Fiber Parameters
Enter the diameter of the fiber in µm
1000
Given
Enter numerical aperture of fiber
0.22
Given
Length of Fiber
Given
Begin the Calculations
Spectrometer Parameters
Enter Dv in degrees
Enter LA in mm (LA = F, Focal Length of Spectrometer)
Grating Area in mm2
12.52
320.00
3364
Given
Given
Calculated
αλ , value of α in
degrees at the
wavelength of interest
15.39
Calculated
βλ , value of β in
degrees at the
wavelength of interest
39.39
Calculated
f/# of spectrometer
5.00
Calculated
NAs is the numerical
aperture of the
spectrometer
f/# of fiber
0.1
2.5
Calculated
Calculated
NAf is the numerical
aperture of the fiber
0.22
Given
Complete Optical Path Optimization for a Czerny- Turner Spectrograph that
Employs a Fiber Optic Cable to Supply Light to the Entrance Slit
•
Step 1. Calculate the entendue of the light source, G
•
=  2
where S = area of light source, mm2 and r = radius of fiber, mm
•
=   2
where G = geometric entendue, S = area of light source, NAf = numerical
aperture of the fiber
S=
7.85E-01
mm
G=
1.19E-01
mm2
Step 2. Calculate the entendue, G, of the spectrometer
Step 2a. Calculate the entendue of the spectrometer assuming a bandpass of
0.5 nm at 500 nm
λ=
600nm
Given
BP =
0.5nm
Given
n=
k=
DV =
1800grooves/mm
1
Given
Given
12.25Degrees
Given
647.7mm
Given
3364mm2
Calculated
α600 =
15.39Degrees
Calculated
β600 =
39.39Degrees
Calculated
LA = F = L B =
GA
f/# spectrometer =
5.0
Calculated
NAs =
0.1
Calculated
f/# fiber =
2.3
Calculated
NAf =
0.22
Given
3.00mm
Given
h=
(G8 x G9)
(G54)
Calculate entrance slit width and area
=
0.5829mm
=
1.74879mm2
Calculate exit slit width
0.5829mm
Finally, calculate G of the spectrometer
1.40E-02
spectrometer
1.19E-01
fiber
Step 3. Re-image light from fiber to match it with the entendue of the monochromator
so that the loss of photons and effect of stray light is minimized.
This involves choosing Lens L1 in Figure 1. This is somewhat arbitrary.
You must choose a focal length and diameter for lens L1
Diameter of Lens L1 in Figure 1 in mm
60
Focal length of Len L1 in Figure 1 in mm
=

2

=

100
=
2
2

2
2
=
Magnification, M
=
= =M
M=
2.2
1 1 1
= +

Solve for p and q
(q = M x p)
p=
q=
145mm
320mm
Solve for d, diameter of lens L1
d=
64mm
Solve for d, diameter of Lens L1
d=
64mm

#   = 2

#  = 2
1
=

1
=

Solve for d, diameter of lens L1
d=
64mm
Solve for d, diameter of Lens L1
d=
64mm
Therefore, all the light from the fiber is collected by a lens, L1,
with an object distance of p mm and will project an image of
the fiber core on the spectrometer entrance slit q mm from
lens, L1
Acknowledgement
Thank you!
Arkansas Space Grant Consortium
Montana Space Grant Consortium
```